TL;DR: Modern TVs absolutely butcher older video sources.

The NES outputs 240p. Most modern TVs see it as 480i (with the i being for interlaced, rather than p for progressive). With interlaced video instead of progressive, a system sends all the odd rows on one frame, then even rows for the next. Modern TVs combine the even and odd rows into a whole frame. (But shows half as many frames per second as a result)

What this means for 240p is that when a tv sees it as 480i, it'll try to do that same frame combination, but on video that isn't split, resulting in blurriness, anything that flashes every other frame being turned into a mess like this, choppier motion, and other bad things.

TVs also try to smoothen out sharp edges, but with 240p video all that does is make it significantly less crisp, And add lag. (Look at the ground in that example image)